Direct evidence of surface exposed water ice in the lunar polar regions

Shuai Lia,b,1, Paul G. Luceya, Ralph E. Millikenb, Paul O. Haynec, Elizabeth Fisherb, Jean-Pierre Williamsd, Dana M. Hurleye, and Richard C. Elphicf

aDepartment of Geology and Geophysics, University of Hawaii, Honolulu, HI 96822; bDepartment of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912; cDepartment of Astrophysical & Planetary Sciences, University of Colorado Boulder, Boulder, CO 80309; dDepartment of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095; eApplied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723; and fAmes Research Center, NASA, Mountain View, CA 94035

Edited by Jonathan I. Lunine, Cornell University, Ithaca, NY, and approved July 20, 2018 (received for review February 8, 2018) Water ice may be allowed to accumulate in permanently shaded water ice because OH may exhibit similar characteristics at UV regions on airless bodies in the inner solar system such as Mercury, wavelengths (15). High reflectance values at 1,064-nm wave- the Moon, and Ceres [Watson K, et al. (1961) J Geophys Res length have also been observed near the lunar poles by the Lunar 66:3033–3045]. Unlike Mercury and Ceres, direct evidence for wa- Orbiter Laser Altimeter (LOLA) and may be consistent with ter ice exposed at the lunar surface has remained elusive. We water ice, but fine particles and lunar regolith with lower degrees utilize indirect lighting in regions of permanent shadow to report of space weathering may also give rise to higher reflectivity at the detection of diagnostic near-infrared absorption features of this wavelength, making this interpretation nonunique (12, 16). water ice in reflectance spectra acquired by the Moon Mineralogy An advantage of near-infrared (NIR) reflectance spectroscopy Mapper [M (3)] instrument. Several thousand M (3) pixels (∼280 × is that it provides a direct measurement of molecular vibrations 280 m) with signatures of water ice at the optical surface (depth of and can thus be used to discriminate H2O ice from OH and H2O less than a few millimeters) are identified within 20° latitude of in other forms (e.g., liquid, surface adsorbed, or bound in min- both poles, including locations where independent measurements erals). NIR reflectance data acquired by the Moon Mineralogy have suggested that water ice may be present. Most ice locations Mapper [M (3)] instrument on the Chandrayaan-1 spacecraft detected in M (3) data also exhibit lunar orbiter laser altimeter provide the highest spatial and spectral resolution NIR data reflectance values and Lyman Alpha Mapping Project instrument currently available at a global scale, including the polar regions. UV ratio values consistent with the presence of water ice and also The wavelength range of M (3) (0.46–2.98 μm) is too limited to exhibit annual maximum temperatures below 110 K. However, properly discriminate OH/H2O species using fundamental vi- only ∼3.5% of cold traps exhibit ice exposures. Spectral modeling bration modes in the 3-μm region (17, 18), and in this study we shows that some ice-bearing pixels may contain ∼30 wt % ice that focus on the detection of diagnostic overtone and combination is intimately mixed with dry regolith. The patchy distribution and mode vibrations for H2O ice that occur near 1.3, 1.5, and 2.0 μm. low abundance of lunar surface-exposed water ice might be associ- Numerical modeling results suggest NIR spectra representing as ated with the true polar wander and impact gardening. The obser- little as 5 wt % (intimate mixing) or 2 vol % (linear areal mixing) vation of spectral features of H2O confirms that water ice is trapped water ice are expected to exhibit all three of these absorptions and accumulates in permanently shadowed regions of the Moon, (Methods and SI Appendix, Fig. S1), although actual detection and in some locations, it is exposed at the modern optical surface. limits in the M (3) data are dependent on instrumental response and signal-to-noise ratios (SNR). lunar polar regions | permanently shaded regions | lunar water ice | The cooccurrence of all three absorptions would be evidence near-infrared spectroscopy | Moon mineralogy mapper for water ice, and M (3) data (optical period 2C) at high latitudes were searched for pixels in shadow whose spectra exhibited these Methods SI Appendix he small tilt of the rotation axes of Mercury, the Moon, and features ( and , Table S1). The resulting EARTH, ATMOSPHERIC, TCeres with respect to the ecliptic causes topographic de- subset of pixels (spectra) was then analyzed using the spectral AND PLANETARY SCIENCES pressions in their polar regions, such as impact craters, to be permanently shadowed from sunlight (1). As a consequence, Significance surface temperatures in these regions are extremely low (i.e., less than 110 K) (1–3) and are limited only by heat flow from the We found direct and definitive evidence for surface-exposed interior and sunlight reflected from adjacent topography (4–6). water ice in the lunar polar regions. The abundance and These areas are predicted to act as cold traps that are capable of distribution of ice on the Moon are distinct from those on accumulating volatile compounds over time, supported by ob- other airless bodies in the inner solar system such as Mercury servations of water ice at the optical surface of polar shadowed and Ceres, which may be associated with the unique forma- locations on Mercury (7–9) and Ceres (10, 11). There are a tion and evolution process of our Moon. These ice deposits number of strong indications of the presence of water ice in might be utilized as an in situ resource in future exploration similar cold traps at the lunar poles (12–14), but none are un- of the Moon. ambiguously diagnostic of surface-exposed water ice, and infer- Author contributions: S.L. designed research; S.L. performed research; S.L. contributed red locations of water ice from different methods are not always new reagents/analytic tools; S.L., P.G.L., R.E.M., P.O.H., E.F., J.-P.W., D.M.H., and R.C.E. correlated. Epithermal neutron counts, for instance, can be used analyzed data; and S.L., P.G.L., and R.E.M. wrote the paper. to estimate hydrogen in the upper tens of centimeters of the The authors declare no conflict of interest. lunar regolith, but such data cannot isolate the uppermost (e.g., This article is a PNAS Direct Submission. optical) surface and cannot discriminate between H2O, OH, or This open access article is distributed under Creative Commons Attribution-NonCommercial- H (14). Ratios of reflected UV radiation measured by the Lyman NoDerivatives License 4.0 (CC BY-NC-ND). Alpha Mapping Project (LAMP) instrument onboard the Lunar 1To whom correspondence should be addressed. Email: [email protected]. Reconnaissance Orbiter (LRO) have been interpreted to in- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. dicate the presence of H2O near the lunar south pole (13), but 1073/pnas.1802345115/-/DCSupplemental. the observed signatures may not be uniquely attributable to Published online August 20, 2018.

www.pnas.org/cgi/doi/10.1073/pnas.1802345115 PNAS | September 4, 2018 | vol. 115 | no. 36 | 8907–8912 Downloaded by guest on October 2, 2021 angle mapping method as a metric to assess the similarity of spectral slopes and absorption features between the M (3) spectra and a laboratory spectrum of pure water frost (Methods). This step relies on the fact that reflectance spectra of water ice exhibit strong “blue” spectral continuum slopes (reflectance decreases with increasing wavelength) (SI Appendix, Fig. S1), whereas typical lunar spectra exhibit an opposite “reddening” effect due to nanophase iron produced during space weathering (19). A spectral angle less than 30° between each M (3) spectrum and the water frost spectrum was empirically determined to define the final subset of M (3) pixels most consistent with the presence of water ice (Methods). Results and Discussion Reflectance measurements in regions of permanent shadow are enabled by sunlight scattered off crater walls or other nearby topographic highs. The shaded regions studied here lie between directly illuminated areas and areas of deep permanent shadow, and the analysis was limited to pixels for which local solar in- cidence angle was greater than 90° to ensure the corresponding surface was in shadow. As expected for areas only receiving in- direct illumination, the SNR of M (3) pixels in these locations is low, and we evaluated the possibility that our process was selecting noisy spectra that mimic ice spectra by random chance. A random dataset was generated that matched the means and SDs of M (3) data in shaded regions near the lunar poles (75° N/S– 90° N/S), but with five times more pixels than M (3) data (∼65 × 106 points). The same procedures were performed on the ran- dom dataset as on the original M (3) data to detect potential ice − absorption features. Only 10 4% of those random points passed our detection criteria, which may indicate the rate of false- positive detections due to random noise. In contrast, ∼0.2% of shaded M (3) data showed positive detections (SI Appendix, Fig. S2C). The average spectrum of positive detections of the random data (SI Appendix, Fig. S3) is distinct from those observed in the M (3) data (Fig. 1), indicating that a population of random noise of a size similar to that of the M (3) data is highly unlikely to produce ice-like spectra. A null hypothesis test was conducted to show that the prediction of a third ice-like absorption based on detection of the other two is significant (SI Appendix, Tables S2 and S3). Water ice must exhibit all three absorptions, and a failure to detect all three casts doubt on its presence. When potential ice spectra were identified in the M (3) data based solely on the presence of two of the three NIR ice absorptions, the third ice- like absorption was always observed in the average spectra of the positive pixels (SI Appendix,Fig.S4). It is thus statisti- cally significant to conclude that the three absorptions near 1.3, 1.5, and 2.0 μm occur simultaneously in a subset of the M (3) data, which is consistent with the presence of water ice in these pixels. The latitudinal distribution of potential ice detections was used as further validation. All M (3) pixels over all latitudes that were locally shaded from the sun at the time of the observations were tested for the presence of the three water-ice absorptions Fig. 1. Example M (3) reflectance spectra of ice-bearing pixels (red) and (shaded surfaces were abundant near the equator when the non–ice-bearing pixels (black) plotted with a laboratory spectrum of pure spacecraft orbit was near the terminator). These data should water ice (blue); solid lines are smoothed spectra based on a cubic spline algorithm (33). exhibit similar instrument noise and systematic errors as polar surfaces in permanent shadow. At low latitudes these data in- clude surfaces that experience high temperatures near local noon Three example M (3) spectra are presented in Fig. 1 for and thus could not support surface ice (i.e., they are not per- possible ice-bearing pixels near the rim of crater Faustini, the manently shadowed). No positive detections at <70° latitude crater De Gerlache in the south pole, and near the crater were observed: only pixels in shaded regions within 20° of each pole showed positive detections, and >90% of the detections Rozhdestvenskiy in the north pole of the Moon (see yellow ar- were located at latitudes within 10° of the pole (SI Appendix, Fig. rows in Fig. 4). The M (3) spectra of possible ice-bearing pixels S2). M (3) spectra exhibiting the cooccurrence of three di- are noisy due to the faint light source in the shaded regions, but agnostic water-ice bands are thus only observed in shadowed absorption features near 1.3, 1.5, and 2.0 μm in these examples regions at high latitudes. are all consistent with those of water ice, whereas similar features

8908 | www.pnas.org/cgi/doi/10.1073/pnas.1802345115 Li et al. Downloaded by guest on October 2, 2021 are not observed in an example spectrum that did not pass the returned lunar samples and most hydrous salts are unlikely to be ice detection criteria (Fig. 1). stable under the vacuum and low-humidity conditions of the The spectra of all ice-bearing pixels were averaged and plotted lunar surface. for the northern (Fig. 2 A and B) and the southern (Fig. 2 C and Alternatively, previous studies found that the OH fundamen- − D) polar regions to further reduce noise. The 1.5-μm absorption tal stretching vibration shifted from ∼2.94 μm(∼3,400 cm 1) for − appears broader and more asymmetric in the average spectrum high-density ice to ∼3.09 μm(∼3,230 cm 1) for low-density ice for the south compared with that from the north (Fig. 2), which is that was condensed from a vapor phase (23). The overtone ab- suggestive of larger grain sizes in the former (20). Spectral sorption in the case of the low-density ice would be expected to mixing model results suggest that the weak absorption near occur near ∼1.55 μm. The apparent 0.05-μm shift of H2O ab- 1.1 μm and the blue slope of the M (3) spectra (Fig. 2) may be sorptions in the M (3) spectra could thus be consistent with the indicative of 30 wt % ice or higher if it is mixed intimately with presence of low-density ice condensed from a vapor phase, a regolith, or over 20 vol % if ice occurs as patches within other- process that would be consistent with water delivered by volatile- wise ice-free regolith (Methods and SI Appendix, Fig. S1). rich impactors or migration of water molecules through the lunar The absorption minima near 1.5 μm of the M (3) spectra of exosphere toward cold traps. However, we cannot fully rule out ice-bearing pixels appear to be shifted ∼0.05 μm to longer the possibility that the 0.05-μm shift [a range of two M (3) wavelengths compared with those of pure ice frost (Figs. 1 and spectral bands] of the 1.5-μm absorptions is due to the low SNR 2). Such band shifts may reflect the increase of hydrogen bond of the M (3) data. strength due to water being bound with minerals (21). However, Potential ice-bearing regions identified in the M (3) data were there was no apparent shift of the absorption near 1.5 μm ob- compared with LOLA reflectance (12), LAMP UV ratio (13), served for olivine (1%) and water-ice (99%) mixtures (22), which and Diviner maximum annual temperature values (24) to pro- may not represent the lunar case where the ice abundance may vide an independent check on whether or not these locations are not be higher than 30%. Although there is no independent evi- consistent with the presence of water ice at the optical surface. dence to support such band shifts are due to molecular water We found that 93.2% of the M-(3)–derived ice locations also bound to the surfaces of minerals that typify the lunar surface, exhibited extreme LOLA reflectance and UV ratio values con- such as pyroxene, plagioclase, olivine, ilmenite, and agglutinate, sistent with the presence of water ice, as well as annual maximum we cannot rule out the possibility that the apparent 0.05-μm shift surface temperatures below 110 K (Fig. 3). The small number of of the 1.5-μm absorption represents water associated with certain candidate locations with slightly higher surface temperatures hydrous minerals as some hydrous salts exhibit water bands close (110–160 K) or lower LOLA reflectance values (0.3–0.32, where to ∼1.55 μm. However, such minerals have not been observed in 0.32 is the mean value near both poles from 75° to 90°) may be EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES

Fig. 2. Average spectra and SDs of ice-bearing pixels in the (A and B) northern and (C and D) southern polar regions from 75° to 90° latitude. In A and C we normalized each M (3) spectrum by its mean reflectance for each ice-bearing pixel to accommodate the variation of the intensity of light scattered onto different pixels, which helps to plot the SD of the whole polar region, whereas the average spectra without normalization are shown in B and D.

Li et al. PNAS | September 4, 2018 | vol. 115 | no. 36 | 8909 Downloaded by guest on October 2, 2021 Fig. 3. (A) Histogram of maximum surface temperatures for ice-bearing pixels (blue) and all shaded pixels from 75° to 90° latitude (black) in the northern polar region and (B) southern polar region. (C) Histogram of LOLA reflectance values for ice-bearing pixels (blue), surfaces with maximum temperature <110 K (green), and all shaded pixels from 75° to 90° (black) in the northern and (D) southern polar regions (E) LAMP “off” and “on” band ratios for ice-bearing pixels (blue), surfaces with maximum temperature <110 K (green), and all shaded pixels (black); only south polar region LAMP data are available. Each dataset is normalized by the total number of pixels in that dataset.

false detections due to noise in M (3) data. The agreement be- (SI Appendix, Fig. S5). No bias of M (3) data acquisition oc- tween these four data sets constitutes a robust detection of water curred at these regions that lack a detection of water ice (SI ice at the optical surface in these locations. Appendix, Fig. S6). We find that the ice stability depth at these The distribution of surface-exposed water ice exhibits strong locations is coincidentally greater than zero when the Moon is spatial coherence with temperatures less than 110 K (SI Ap- hypothesized to be on its paleoaxis (SI Appendix, Fig. S7) (25), pendix, Fig. S5), suggesting that temperature is one of the major which indicates that surface ice may only be retained at long- controlling factors. However, not all regions less than 110 K timescale cold traps associated with the polar wander, similar to (cold traps) show ice exposures, such as cold traps in craters what has been proposed for the dwarf planet Ceres (11). Amundsen, Hedervari, Idel’son L, and Wiechert near the south The patchy distribution and low abundance of surface-exposed pole; the cold trap in Bosch crater and most micro cold traps water ice in lunar cold traps may reflect a low rate of water near 330° longitude between 80° and 85° N near the north pole supply and a fast rate of regolith gardening process. The Moon is

8910 | www.pnas.org/cgi/doi/10.1073/pnas.1802345115 Li et al. Downloaded by guest on October 2, 2021 Fig. 4. Distribution of water-ice-bearing pixels (green and cyan dots) overlain on the Diviner annual maximum temperature for the (A) northern- and (B) southern polar regions. Ice detection results are further filtered by maximum temperature (<110 K), LOLA albedo (>0.35) (12), and LAMP off and on band ratio (>1.2, only applicable in the south) (13). Each dot represents an M (3) pixel, ∼280 m × 280 m.

hypothesized to have rotated on its current axis 2–3 Ga ago (25). (∼30 wt %). Thus, the delivery, transport, and/or retention of Since then, no significant amount of ice may have accumulated volatiles at the optical surface of the Moon are distinct from at newly formed cold traps (i.e., Amundsen, Hedervari, Idel’son, other inner solar system objects that have similar cold traps at Wiechert, and Bosch), which suggests that the water supply is their poles. Understanding the physical processes responsible for very slow and the observed ice is very old (older than the time these differences and the timescales on which they operate, in- period of polar wander). It is also possible that any new accu- cluding regolith gardening, deposition mechanisms (impact de- mulated ice (formed after true polar wander) is thin due to the livery, volcanic outgassing condensation, and water migration), low rate of supply. Simulations of impact gardening suggest that and potential evolution of cold traps due to true polar wander a layer of frost may last no longer than 20 My on the lunar (25), will be a fertile area of future research for understanding surface (26). However, it is unclear whether the solar wind volatile behavior in the inner solar system. bombardment, galactic cosmic rays, and the interplanetary me-

Methods EARTH, ATMOSPHERIC,

dium UV can cause substantial loss of ice over the geological AND PLANETARY SCIENCES timescale (2, 27–29). The gardening effect of impacts may mix Potential ice absorption features in surface reflectance spectra near the lunar surface-exposed ice with regolith more efficiently than the ac- poles (75° N/S–90° N/S) were searched for using data acquired by the M (3) cumulation of “new” ice after the proposed true polar wander (30). The M (3) radiance data acquired during the optical period 2c were and result in the observed low ice abundance. downloaded from the Planetary Data System and corrected for thermal contributions using the methods of Li and Milliken (31), although such ef- The distribution of locations that meet the criteria for the M fects are negligible in shaded regions near the lunar poles. Processed data (3), LOLA, Diviner, and LAMP (data for southern pole only) were binned at a resolution of 128 pixels per degree and then mosaicked data sets (Fig. 4) reveals that the southern polar region exhibits a from 75° to 90° N/S using a stereographic polar projection and globally using great number of ice-bearing M (3) pixels than the north because a simple cylindrical projection. Water ice has four diagnostic absorption of more shaded regions in the former (SI Appendix, Fig. S2). Ice features centered near 1.1, 1.3, 1.5, and 2.0 μm at the 1.0–2.5-μm region (20), detections in the south are clustered near the craters Haworth, the latter three of which were applied as criteria to assess whether M (3) Shoemaker, Sverdrup, and Shackleton, while those in the north spectra show ice absorption features. In this study we focus on M (3) spectral are more isolated. Our ice detections near both lunar poles ex- bands between 1.0 and 2.5 μm due to considerations of signal-to-noise hibit no bias between the near side and far side (Fig. 4), while the (see SI Appendix for detailed justification of using spectral bands at this wavelength range). former may have been affected by earthshine, which suggests The search for ice focused on shadowed areas that were indirectly illu- that our ice detections received negligible or no effects from ∼ minated by sunlight that had been reflected from nearby, directly illuminated earthshine. In total, only 3.5% of cold traps at both lunar poles topography. Such reflected light can include spectral reflectance information

exhibit ice signatures, reinforcing the distinction between the of the surface material in direct illumination. The true reflectance spectra (RT) Moon and other bodies such as Mercury and Ceres where near- in shaded regions can be calculated as surface ice distribution appears to be controlled primarily by temperature and thus more common in cold traps. In addition, = I RT ð =πÞ α , [1] deposits of nearly pure water ice (100% water ice) are inferred J R for cold traps on Mercury (7, 8) and Ceres (10), whereas the where I is the radiance captured by the sensor, J is the solar irradiance lunar equivalents are suggestive of much lower abundances of ice spectrum, R is the bidirectional reflectance at locations where the sunlight is

Li et al. PNAS | September 4, 2018 | vol. 115 | no. 36 | 8911 Downloaded by guest on October 2, 2021 scattered, α is the amount of light scattered into the shaded region which and the continuum determined by the two shoulder points on either side of depends on the local topography and phase angle and varies from pixel to the absorption. Although any absorption with an absorption depth greater pixel. The variation of α will not introduce any absorptions and is only im- than zero was considered, only those spectra with absorption center posi- portant for quantitative analysis of ice abundance. In this study, α is set to 1 tions and shoulders within the range listed in SI Appendix, Table S3 were because we emphasize the global and qualitative assessment of water ice in counted as possible ice detections. the lunar polar regions. We assumed R to be the average reflectance spectra The second step assessed the spectral angle (SA) between M (3) pixels of illuminated regions near the poles (75° N/S–90° N/S) (SI Appendix, Fig. S8). identified in step 1 and laboratory spectra of pure water frost. VIS-NIR re- The local solar incidence angle (i) was applied as the criterion for de- flectance spectra of water ice exhibit strong blue continuum slopes (SI Ap- termining whether a pixel was shaded (i ≥ 90°) or illuminated (i < 90°). pendix, Fig. S1), a trend that is opposite of typical lunar spectra that exhibit The M (3) solar incidence angles were derived using a ray-tracing model in conjunction with the LOLA topography data (30) and could be applied to spectral reddening effects due to the presence of nanophase iron formed determine shaded or illuminated M (3) pixels. Shaded pixels identified by during space weathering (19). The SA metric can be used to assess the sim- this method were also verified by visually checking the M (3) images. ilarity between two spectra, including spectral slopes and absorptions. The Radiative transfer modeling results (32) suggest that four diagnostic spectral angles between individual M (3) spectra and spectra of pure water water-ice absorptions at 1.1, 1.3, 1.5, and 2.0 μm may be detectable in NIR frost (Fig. 1) were calculated to assess the similarity of their spectral shapes, reflectance spectra of intimately mixed ice–regolith mixtures that con- defined as tain >30 wt % ice, whereas the three longer wavelength (and stronger) 0 1 * * absorptions should be observed for ice contents >5wt%(SI Appendix, Fig. · −1@ M I A – SA = cos * * , [2] S1). If ice regolith distribution is spatially heterogeneous and more akin to an areal (checkerboard) mixture at the subpixel scale, then spectral mixing M I may exhibit linear behavior. In this scenario, linear mixing results indicate * * where M is the vector of M (3) spectra; I is the vector of the spectrum of that spectra for surfaces with >5 vol % ice should exhibit all four absorp- pure water frost. A 0° spectral angle means that the two vectors are parallel tions, whereas the stronger three features would be observable for surfaces (spectrally similar), whereas a 90° spectral angle means that the two vectors with >2 vol % ice (SI Appendix, Fig. S1). The three stronger (longer wave- < length) absorptions were used as criteria to examine whether any are perpendicular (spectrally dissimilar). We found that spectral angles 30° individual M (3) spectra showed evidence for water ice, but the centers and may be indicative of the presence of water ice, thus only pixels (spectra) widths of these features can vary with particle size (20). The band center and from step 1 with values below this threshold were considered ice-bearing. shoulder positions (widths) of ice absorptions for 50–2,000-μm particle sizes The 30° threshold was determined by examining the spectral angles of hand- were characterized by Clark (20) (SI Appendix, Table S1) and were used as picked ice-bearing and ice-free M (3) spectra. Original M (3) spectra of additional criteria to examine M (3) spectra in shaded regions. possible ice-bearing pixels that met these criteria were then averaged Potential ice-bearing M (3) pixels were identified in two steps. First, pixels (without smoothing) for the lunar southern and northern polar regions in shaded regions whose spectra exhibited three absorption features (75° N/S–90° N/S), respectively. matching those in SI Appendix, Table S1 were identified. Cubic spline smoothing (33) was applied to M (3) spectra to help identify absorption ACKNOWLEDGMENTS. We thank Dr. Roger Clark, Dr. Tim Glotch, and an features in this step. Spectral continua of the upper and lower bounds of anonymous reviewer for their fruitful comments. We also thank Dr. Roger smoothed M (3) spectra were calculated, where the former highlight ab- Clark for pointing out the shift of the 1.5-μm absorption, which has signif- sorption shoulders and the latter define absorption centers. Absorption icantly improved the quality of this paper. We are grateful to Dr. Oded strength was calculated as the distance between the absorption center point Aharonson for the discussion of the statistical test in this work.

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8912 | www.pnas.org/cgi/doi/10.1073/pnas.1802345115 Li et al. Downloaded by guest on October 2, 2021